Global Smooth Solutions of Euler Equations for Van der Waals Gases

We prove global in time existence of solutions of the Euler compressible equations for a Van der Waals gas when the density is small enough in Hm, for m large enough. To do so, we introduce a specific symmetrization allowing areas of null density. Next, we make estimates in H m, using for some terms the estimates done by Grassin, who proved the same theorem in the easier case of a perfect polytropic gas. We treat the remaining terms separately, due to their nonlinearity. 2000 Mathematics Subject Classification: 35L60, 35Q31, 76N10.